Q. The area bounded by $|x - 1| \leq 2\ and\ x^{2} - y^{2} = 1$, is
A) $6\sqrt{2} + \frac{1}{2}\log{|3 + 2}\sqrt{2}|$
B) $6\sqrt{2} + \frac{1}{2}\log{|3 - 2}\sqrt{2}|$
C) $6\sqrt{2} - \log{|3 + 2}\sqrt{2}|$
D) None of these
Explanation
(c)
Required area
$= 2\int_{- 1}^{3}{\sqrt{x^{2} - 1}\ dx}$
$= 2\left\lbrack \frac{x\sqrt{x^{2} - 1}}{2} - \frac{1}{2}\log{|x + \sqrt{x^{2} - 1}} \right\rbrack_{- 1}^{3}$
$= \left( x\sqrt{x^{2} - 1} - \log{|x +}\sqrt{x^{2} - 1}| \right)_{- 1}^{3}$
$= 6\sqrt{2} - \log{|3 + 2\sqrt{2}|}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.